The Cartan distribution on an infinite jet bundle is the differential-geometric distribution, meaning a smoothly varying choice of subspace of each tangent space, spanned by the total derivative vector fields. These vector fields differentiate the independent variables together with all derivative coordinates in a way consistent with prolongation, the process of adjoining equations for all derivatives of the original equations. Their Lie brackets remain in the distribution, so the Cartan distribution is an involutive distribution.
For a system of partial differential equations, the Cartan distribution restricts to its infinite prolongation, the subset of the infinite jet bundle on which the equations and all their differential consequences hold. Its integral manifolds are the prolonged graphs of solutions, obtained by recording a solution together with all of its derivatives. A diffiety consists of such an infinite-dimensional equation manifold, namely the manifold defined by these prolonged equations, together with this distribution.
